The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé–Kuratowski convergence

In this paper, we obtain the Painleve–Kuratowski upper convergence and the Painleve–Kuratowski lower convergence of the approximate solution sets for set optimization problems with the continuity and convexity of objective mappings. Moreover, we discuss the extended well-posedness and the weak extended well-posedness for set optimization problems under some mild conditions. We also give some examples to illustrate our main...